Part of it has to do with what you said here: even being Aragorn's wife and Queen of Gondor, she goes to the land of her people to die. But there is nothing waiting for her once she gets there, and in a way she dies isolated from both the world of men and the world of elves. I think it's a striking ending not just to LotR but to the entire legendarium. Nothing more to tell after that.

If this sounds too bleak, however, I do believe Galadriel had foreseen Arwen's passing in Lórien, and might have prepared Cerin Amroth to "take her in", as it were, as a kind of final passing of the torch between the "morning" and the "evening star" of Elven women.